How do you multiply #(4x-5)(2x^5 + x3 - 1)#?

1 Answer
George C.
Jul 26, 2015

For each power of #x# from #x^6# down to #x^0#, pick out the pairs that multiply to give that power and add them to find:

#(4x-5)(2x^5+x^3-1)#

#= 8x^6-10x^5+4x^4-5x^3-4x+5#

Explanation:

Looking at each power of #x# in turn from #x^6# down to #x^0#, pick out the pairs that multiply to give a term with that power of #x#:

#x^6# : #4x*2x^5 = 8x^6#

#x^5# : #-5*2x^5 = -10x^5#

#x^4# : #4x*x^3 = 4x^4#

#x^3# : #-5 * x^3 = -5x^3#

#x^2# : none

#x# : #4x*-1 = -4x#

#1# : #-5*-1 = 5#

Add to get:

#8x^6-10x^5+4x^4-5x^3-4x+5#

Normally when multiplying two polynomials in this way you would have two pairs to multiply and add for most of the powers of #x#, but a similar approach works.

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